Joe and Tom play a shooting game. The match consists of 7 games. Whoever wins 4 games first will win. Probability that Joe wins a game = 0.6. Draws are not allowed for any game. Find :
(1) Probability that Joe wins the match.
(2) Given that Joe wins the match, find probability that Tom has won 2 games.
Probability
2010-12-24 3:18 am
回答 (2)
2010-12-24 3:45 am
✔ 最佳答案
Note that P(Tom wins a game) = 1 - 0.6 = 0.41)P( Joe wins the match)= P(End with 4 games and Joe wins the last game)
+ P(End with 5 games and Joe wins the last game)
+ P(End with 6 games and Joe wins the last game)
+ P(End with 7 games and Joe wins the last game)= 0.6^4
+ (4C3)(0.6^3)(0.4) (0.6)
+ (5C3)(0.6^3)(0.4^2) (0.6)
+ (6C3)(0.6^3)(0.4^3) (0.6)= 0.1296
+ 0.20736
+ 0.20736
+ 0.165888= 0.710208= 11097/15625
2)P(Joe wins the match and Tom has won 2 games)= 0.20736 / 0.710208= 0.291970803= 40/137
2010-12-23 19:53:47 補充：
P(Joe wins the match and Tom has won 2 games)
= P(End with 6 games and Joe wins the last game) / P( Joe wins the match)
2010-12-24 3:26 am
Prob that Joe wins=0.6 & Tom wins =0.4
1) Prob = 0.6*0.6*0.6*0.6 = 0.1296
2) Prob = 0.1296*0.4*0.4 = 0.0207
1) Prob = 0.6*0.6*0.6*0.6 = 0.1296
2) Prob = 0.1296*0.4*0.4 = 0.0207
參考: me
收錄日期: 2021-04-21 22:17:59
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https://hk.answers.yahoo.com/question/index?qid=20101223000051KK01073